Java: Keep executing if statement

The easiest approach would be to use a Timer. With that, you don't need the if logic; you can just use the firstTime argument when scheduling a TimerTask.

Timer timer = new Timer();
TimerTask task = new TimerTask() {
    @Override
    public void run() {
        // do something
    }
};
// schedule the task to be run every 100ms (0.1 sec),
// starting after "threshold" milliseconds have past
timer.schedule(task, threshold, 100);

It's not clear from your description if you want to repeatedly "do something" once the time threshold has been exceeded, or if you just want to wait until a certain time has passed and then "do something" once. The above code is for the repeating case. For a one-shot occurrence at some future time, change the last line to:

timer.schedule(task, threshold);

If you're using Swing, you should use a Swing Timer rather than a java.util.Timer. See How to Use Swing Timers for more info.

EDIT: Your comment clarified things a bit. It's fairly easy to do what you described:

Timer timer = new Timer();
TimerTask task = new TimerTask() {
    private final long start = System.currentTimeMillis();
    @Override
    public void run() {
        if (System.currentTimeMillis() - start < threshold) {
            // do something
        } else {
            // do something else
        }
    }
};
// schedule the task to be run every 100ms (0.1 sec), starting immediately
timer.schedule(task, 0, 100);

Note that "do something" and "do something else" can be method calls to an enclosing class.

A cleaner approach might be to define several TimerTasks that are scheduled to execute at different times. The "something else" task that triggers an exception can be scheduled for one-time execution at the threshold time. You can also cancel individual tasks and you can even schedule a task that will cancel another task.